Inspired by Vogan's lambda norm, the second named author introduced spin norm in his 2011 HKUST thesis. See [1]}. In the current setting, the spin norm of the \(K\) -type \(E_{\mu }\)  specializes as
\(\Vert \mu \Vert _{\rm spin} =\min _{0\le j \le 62}\Vert \lbrace \mu -\rho _n^{(j)}\rbrace +\rho _c\Vert .\) 
